Pith Number

pith:H762V54L

pith:2010:H762V54LCYQ3UMUZ2FRIZLMQXP

not attested not anchored not stored refs pending

Ternary cubic forms having bounded invariants, and the existence of a positive proportion of elliptic curves having rank 0

Arul Shankar, Manjul Bhargava

arxiv:1007.0052 v2 · 2010-07-01 · math.NT

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{H762V54LCYQ3UMUZ2FRIZLMQXP}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Receipt and verification

First computed	2026-05-18T03:03:57.178295Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3ffdaaf78b1621ba3299d1628cad90bbd1c9a1fa37a33364cafecbbde0775d3e

Aliases

arxiv: 1007.0052 · arxiv_version: 1007.0052v2 · doi: 10.48550/arxiv.1007.0052 · pith_short_12: H762V54LCYQ3 · pith_short_16: H762V54LCYQ3UMUZ · pith_short_8: H762V54L

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/H762V54LCYQ3UMUZ2FRIZLMQXP \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 3ffdaaf78b1621ba3299d1628cad90bbd1c9a1fa37a33364cafecbbde0775d3e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "bb679280531539af97cd056c02496f5dbe25ab0cd617708a4486ce3ee9741fe9",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2010-07-01T00:19:19Z",
    "title_canon_sha256": "3712e46bb1f307f193c558da87cd8e257a778b9db54649da5d16e32f6204643c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1007.0052",
    "kind": "arxiv",
    "version": 2
  }
}